The workers at the Marel factory are filling up their lunch trays with salads, sausages and pickled fish when the presidential candidate arrives, spouse and new baby in tow. The canteen has seen several such visits from some of the six hopefuls in the running for Iceland's election on Saturday. Today's guest is frontrunner to unseat President Ólafur Ragnar Grimsson, 69, who has been in office for a record 16 years.

Aged 37, and with a successful career as a broadcast journalist, Thóra Arnórsdóttir entered the race in March. She was then seven months pregnant. But she collected the necessary 1,500 signatures for her candidacy in a single day and has led the polls ever since, even after taking weeks out of campaigning to give birth to her third child with partner Svavar Halldórsson, who also worked in television, and who now carries the baby at the back of the Marel canteen.

In her speech she tells the workers that she wants to be a non-partisan president. "My personal experience behind the scenes of politics while working in the media has left me with absolutely no interest in participating in party politics at all," she says later.

"The role of president has to be about representing all Icelanders, about uniting people, all the people, and to encourage the stability and trust that we lost in the crash." It was in 2008 that all three of Iceland's commercial banks collapsed, taking the country to the brink of bankruptcy.

As European countries now stare into their economic abyss, Iceland has already been there and is on its way back up, leading some to suggest it should be a blueprint for other nations.In two referendums Icelanders refused to pay the foreign debts of what were, after all, private – not state-owned – banks. They turfed out the politicians who had not seen the crash coming and put several bankers on trial.

The country kept the progressive theme going by electing Jóhanna Sigurðardóttir prime minister, the world's first openly lesbian world leader. Key positions were taken by women, including finance minister and speaker. A 2011 cabinet reshuffle saw women outnumbering men for the first time in Iceland's history. And the Church of Iceland just elected its first woman leader, Bishop Agnes Sigurðardóttir.

But as impressive as that looks compared with Britain, where just 20% of the cabinet is female, Arnórsdóttir says Iceland is not yet an egalitarian utopia. "While we do have a lot of women at the top, this doesn't necessarily reflect the experience of working women at all levels. There is still a big salary gap.

"I don't think there's a blueprint here. We are just 320,000 people and we know that in the years before the crash some in Iceland, the president included, had become too full of themselves.

"We thought we were superior because of the Viking spirit and all that, but it turned out we had just been sloppy in our way of doing things. The banking sector, we found out the hard way, did not suit us.

"It has been tough and still is. The effects are still being felt, we've had cuts and people are still losing their homes, we have unemployment, a new phenomenon for Iceland. But I think we can say with confidence that we are back on the right track. Our roots are deep. The crash has been an opportunity to engage in a conversation, to make a clean sweep."

Later, at the couple's modest new home outside Reykjavik, her partner apologises for the clutter and unopened boxes and puts his feet up on the coffee table with his laptop on his knee. "We had hoped to be organised and settled in by now. In time to enjoy the Euro 2012. Then someone decided to run for president," he said with a grin.

He is inputting the questions Arnórsdóttir was asked that day, to be answered in future speeches. "Our achilles heel is that she is not rude. She decided she would only run if she could run clean." The couple are, outwardly at least, relaxed about Saturday's election. "She's young and blonde," Halldórsson shrugs, "so we knew there would be a lot of attention, but this is Iceland: our lives do not have to be turned upside down. If she is president, the children will go to the same school, that car outside will still be the family car."

Arnórsdóttir was urged to stand by voters angered at the president's decision to run for re-election, despite being widely expected to retire.

"I started getting a few letters. I considered it really nice of people I didn't know. I thought I'd keep the letters to show the kids when they were older. Then it became an avalanche. So I thought, maybe this is something I have to consider. We had great jobs, a beautiful family, just bought a house: it was definitely not in the plan. But life is full of surprises.

"Its been a once-in-a-lifetime experience," she said. Sitting in the small kitchen where Jamie Oliver cookbooks are piled on top of a fridge whose door is pasted with handwritten memos, Thóra breastfeeds the baby while having her makeup applied for a magazine photoshoot.

She has already given three speeches without notes today. Alongside the factory, there was an old people's home where there was dancing. "It was fun," she said with a smile.

It hasn't all been plain sailing. There have been damaging rumours that she would immediately take maternity leave if elected, Halldórsson's 20-year-old conviction for being involved in a drunken brawl has been raked over, and there have been the predictable suggestions that she should stay at home with her children.

"As a woman I know I could, would and should expect it," says Arnórsdóttir. "It's amazing that [as a society] we haven't advanced as much as we thought, because this rhetoric is very much going on out there, with people saying, 'She should be at home with her children'. But very few say it directly to us.

"I'm not saying it's easy, but the key thing is that because a woman is of child-bearing age or has children, they should not be automatically excluded from top posts. That doesn't make sense. No one suggests men who are fathers shouldn't hold positions of power.

"He [Halldórsson] gets kind of offended, this is his sixth child, [he has three daughters from a previous relationship]. He's really good at this, he's 42 and if he chooses to stay at home with his children, which is after all a privilege, then he should be able to make that choice.

"Gender equality is not just about women's rights. It's also about men's choices, without the view that he has sacrificed his life or career or is somehow feminine or less of a man," she said.

"I can still repair the car," yells Halldórsson from the next room. And cook, adds his partner.

"It's the most natural thing in the world to have a baby," she said. "It doesn't mean you have to stop living. My experience is that older women have the attitude, 'I'm not voting for your kids, I've voting for you'. It's more the younger women who are having the issue. I've never had a man ask me about the children.

"The younger men and women seem to be more chauvinistic than the older generation, which is worrying."

The baby fed and asleep, Arnórsdóttir consults her cousin Asdis on what earrings she should wear for the photoshoot.

Asdis is one of those many young Icelanders who left to study abroad. She came home to help with the campaign. "I hoped and hoped she would run. It's truly been something, getting round and meeting all sorts of people and seeing places. Thóra has made me very proud to be an Icelander and to be a girl. It feels like I'm working for the good guy."